A Well-Balanced Shallow Flow Solver for Coastal Simulations

Run-up, characterized by moving shoreline over irregular sloping bed, is an important coastal process that should be accurately simulated to provide guidelines for coastal designs. This paper presents and tests a finite volume Godunov-type shallow flow model for simulating coastal run-ups and other processes. A well-balanced numerical scheme is constructed for applications involving moving shoreline. The model is validated against several benchmark tests. Results are compared with analytical solutions and experimental measurements and close agreement is achieved for all of the cases. This indicates the potential of the model in practical simulations of wave run-up and other coastal hydrodynamics.